Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circles?

What is a Bowsprit?

A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowsprit which is 6 ft above the water.

Flying High

How high above the earth must a person be raised that he [or she] may see 1/3 of its surface?

Small Fish

There is a fish whose body weighs 8 ounces. How much does the whole fish weigh?

Perpendicular Curves

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

A Hole in One?

A barrel has various holes in it. The first hole empties the barrel in three days...

Out to Pasture 2

X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?

Fields of Grain

I have two fields of grain. From the first field I harvest 2/3 sila (a measurement of grain volume) per sar (a unit of area); from the second, 1/2 sila per sar.

Logarithms: The Early History of a Familiar Function

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

The Door is Ajar

A two door gate of unknown width is opened so that a 2 ts'un gap exists between the two doors.